We understand both motion and rest are relative. But me and my friends always discussing about this kind of thought experiment involving a single object (for example, a particle with mass or massless particle) with nothing else existed (no other objects, no force, no gravity, no quantum field, etc.). Because motion is relative, then someone can say the lone object is at rest. It is motionless, and someone can also say the natural state for this lone object is to be at rest. But for me, in my opinion this kind of thought experiment is actually impossible in reality and this thought experiment is purely imaginative. It is impossible and irrational because both motion and rest (motionless) are relative so this lone object with nothing else existed is actually neither moving nor not moving thus a single object universe is purely imaginative. What do you think?
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1$\begingroup$ Massless particles can never be at rest. E.g. Photons will always travel at the speed of light relative to everything else. On the other hand, for a particle with mass there will always be a reference frame relative to which the particle is at rest. Actually, the mass of the particle is the mass measured in the reference frame in which the particle is at rest. $\endgroup$– NemoCommented Oct 9, 2017 at 9:17
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$\begingroup$ Another reason why this kind of thought experiment is impossible is, let's say for the sake of discussion, that the lone object is absolutely motionless and the lone object is an object with mass with nothing else existed (no gravity, no force, no quantum field, everything, etc. besides the lone object), what makes that lone object to be at rest? Is it something external or internal? If it is because of something internal, then the single object universe is irrational. If it is something external, then the assumption is irrational too. So, that means there must be a multiplicity of objects. $\endgroup$– SnoopyKidCommented Oct 9, 2017 at 9:24
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1$\begingroup$ I think that in this kind of Universe (Single-particle Universe) motion cannot be defined. In general, an object is considered to be at rest relative to a reference frame if the object is not moving with respect to that frame. But in this hypothetical Universe there is no other object relative to which the considered object can be at rest or in motion. $\endgroup$– NemoCommented Oct 9, 2017 at 9:36
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$\begingroup$ My friend say it is possible for the single object to be at rest with zero velocity, zero friction or zero net force, for example like an apple stays still on a table. But he doesn't aware at all that the apple is at rest in relation to the table and gravity is still acting on both of these objects (i.e, apple and table). In order for the single object to be at rest, there must be something other than the single object so it is possible for the single object to be motionless. Motion is always there and there are always a multiplicity of objects. What do you think? $\endgroup$– SnoopyKidCommented Oct 9, 2017 at 10:59
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$\begingroup$ Ask your friend: What does it mean for a single object to be at rest, what does it mean to have zero velocity? The whole notion of "being at rest" or being in motion makes sense only if there is something relative to which you can have that state of motion. So I think you're on the right path. This is getting way too philosophical, but it is also important if this kind of Universe is finite or infinite because if it is finite, you can have a state of motion relative to the edge of that Universe. $\endgroup$– NemoCommented Oct 10, 2017 at 8:37
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You're right, motion is only a relative concept and without another reference body (or what we physicists would call a "reference frame") the notion of motion cannot really be defined. A fundamental but often implicit assumption in physics is that measurement can be made and reproduced. Only with measurement then we can unambiguously and meaningfully describe our physical world and talk about physics at all. But to make meaningful measurements, you unavoidably need to bring in a measurement device hence a reference body to your universe. So your question is really more a philosophical one than a physical one.
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$\begingroup$ Of course, my friend is still defending this kind of thought experiment by saying this thought experiment is possible in reality and the single object is necessarily at rest without any force at all and it is at rest all by itself. Whereas, both motion and motionless are relative. $\endgroup$ Commented Oct 9, 2017 at 11:01
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$\begingroup$ Tell him that, at least, he should be there too $\endgroup$ Commented Oct 9, 2017 at 12:30
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$\begingroup$ The point is with the whole universe consists of only that single object, that universe will only have one single physical law - "there exists this object." - and nothing else. So if you don't even have the physics of motion in that universe, how can you talk about the "motion" occurs in there? Well, again this is really more philosophy than physics. $\endgroup$– AstroKCommented Oct 9, 2017 at 18:09